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Find the minimum value of the function
f(x)=2x^(2)-25.8 x+89.7 to the nearest hundredth.
Answer:

Find the minimum value of the function $f(x)=2 x^{2}-25.8 x+89.7$ to the nearest hundredth. $\newline$ Answer:

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Find trigonometric functions using a calculator

Full solution

Q. Find the minimum value of the function

f(x)=2 x^{2}-25.8 x+89.7

to the nearest hundredth.

\newline

Answer:

Identify function type: Identify the type of function. $\newline$ The function $f(x) = 2x^2 - 25.8x + 89.7$ is a quadratic function in the form of $f(x) = ax^2 + bx + c$ , where $a$ , $b$ , and $c$ are constants.
Determine parabola vertex: Determine the vertex of the parabola. Since the coefficient of $x^2$ is positive ( $a = 2$ ), the parabola opens upwards, and the vertex represents the minimum point of the function.
Calculate x-coordinate: Calculate the x-coordinate of the vertex. $\newline$ The x-coordinate of the vertex of a parabola given by $f(x) = ax^2 + bx + c$ is found using the formula $-\frac{b}{2a}$ . $\newline$ For our function, $a = 2$ and $b = -25.8$ , so we have: $\newline$ $x = -(-25.8) / (2 \cdot 2) = \frac{25.8}{4} = 6.45$
Calculate y-coordinate: Calculate the y-coordinate of the vertex. $\newline$ To find the y-coordinate of the vertex (which is the minimum value of the function), we substitute $x = 6.45$ into the function: $\newline$ $f(6.45) = 2(6.45)^2 - 25.8(6.45) + 89.7$
Perform calculations: Perform the calculations. $\newline$ $f(6.45) = 2(41.6025) - 25.8(6.45) + 89.7$ $\newline$ $f(6.45) = 83.205 - 166.41 + 89.7$ $\newline$ $f(6.45) = -83.205 + 89.7$ $\newline$ $f(6.45) = 6.495$
Round to nearest hundredth: Round the result to the nearest hundredth. $\newline$ The minimum value of the function to the nearest hundredth is $6.50$ .

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